Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2350 conjugacy classes of subgroups.
The subgroup lattice has 402 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C47 | C22⋊C4 |
| commutator | C22 | C22×C42×C47 |
| Frattini, cosocle | C24 | C24×C47 |
| socle | C23×C47 | C2×C22⋊C4 |
| prime radical | C25×C47 | C23 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C47 ◁ C24×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C47×#1740 | C2 | direct (N × H) |
| 11. C2×#117×C47 | C4 | semidirect |
| 12. C2×#117×C47 | C4 | semidirect |
| 16. C22×C4⋊C4×C47 | C4 | semidirect |
| 20. C22×C42×C47 | C4 | semidirect |
| 41. #117×C47 | C2×C4 | semidirect |
| 46. C2×C4⋊C4×C47 | C2×C4 | semidirect |
| 60. C2×C42×C47 | C2×C4 | semidirect |
| 162. C2×#1740 | C47 | direct (N × H) |
| 194. #1740 | C2×C47 | direct (N × H) |
| 202. C2×C47 | #1740 | direct (N × H) |
| 211. C2×#117 | C4×C47 | semidirect |
| 212. C2×#117 | C4×C47 | semidirect |
| 216. C22×C4⋊C4 | C4×C47 | semidirect |
| 220. C22×C42 | C4×C47 | semidirect |
| 222. C47 | C2×#1740 | direct (N × H) |
| 242. #117 | C2×C4×C47 | semidirect |
| 247. C2×C4⋊C4 | C2×C4×C47 | semidirect |
| 261. C2×C42 | C2×C4×C47 | semidirect |
| 398. C2 | C47×#1740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#117×C47 | 2 |
| C47×#1740 | 2 |
| C2×C47×#342 | 2 |
| C2×#1740 | 47 |